{"id":"7fbde968-7a45-43a2-ad65-13dd3ebdbe1f","arxiv_id":"2608.09753","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Moving an Fe atom across 225 binding sites on 2H-NbS2 reveals Yu-Shiba-Rusinov energy shifts covering about 70% of the superconducting gap, attributed to local crystal-field modulations from hidden lattice distortions.","lead":"Using a scanning tunneling microscope, researchers moved single iron atoms across the surface of the superconductor 2H-NbS2 and found that the energy of their Yu-Shiba-Rusinov excitations varies strongly from site to site, even where the surface looks perfectly uniform. The variation is attributed to hidden distortions of the crystal lattice near intrinsic defects, suggesting a new way to image nanoscale lattice modulations that standard microscopy misses.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The core attribution rests on a single-spin YSR formula, but the Fe sensor is explicitly multiorbital; unmeasured site-to-site changes in spin state or magnetic anisotropy could shift εγ without the claimed exchange-coupling variation, so the inference to Nb displacements is not yet established.","rationale":"The reader's weakest assumption identifies the same load-bearing point: the single-spin YSR model is applied to a multiorbital Fe atom. I agree with that concern, with one nuance: site-to-site changes in magnetic anisotropy or spin state would themselves be crystal-field effects, so the broad claim that 'variations in the local crystal-field environment' matter could survive. What is directly threatened is the more specific narrative that the shifts arise from exchange-coupling variations caused by Nb displacements. The paper's exclusion of LDOS, gap, and potential-scattering variations is careful and the measurement itself appears strong; the weak point is the model used to convert the YSR energy map into a lattice-distortion map. The proposed check—fitting the full multiplet with a spin Hamiltonian that allows anisotropy and spin-state variations—would settle whether the exclusion argument actually isolates J. Because the reader already judged the paper CONDITIONAL on essentially this basis, my stress-test does not move the verdict. No machine-checked proofs or released code are available, and the Zenodo data would be needed for the proposed re-analysis; this further supports a conditional rather than unconditional acceptance.","tokens_in":18802,"tokens_out":7542,"duration_ms":69874,"concrete_test":"Take the 225 deconvolved spectra (or a representative subset spanning the full εγ range) and fit the complete α–δ multiplet with a multiorbital spin Hamiltonian that independently varies S, uniaxial anisotropy D, transverse anisotropy E, orbital-dependent exchange couplings, and potential scattering. Then test whether the observed εγ variation can be reproduced with the exchange couplings held constant while only anisotropy/spin parameters vary. If yes, the exclusion argument in Sec. II C does not single out exchange-coupling/lattice-distortion variations; if no, the conclusion is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II C concludes that, because the superconducting gap is uniform, the LDOS at each site is uncorrelated with εγ, and the YSR asymmetry (potential scattering) is small, the only remaining variable in Eq. (1) is the exchange coupling J, whose spatial variation is then interpreted as crystal-field/lattice modulations. This is an exclusion argument built on the classical single-spin formula εYSR = Δ(1−A^2+B^2)/sqrt((1−A^2+B^2)^2+4A^2), with A = π S ρ0 J/2 and B = π ρ0 K. However, the Fe atom is not a single classical spin: the paper itself identifies four YSR pairs (α–δ) originating from crystal-field-split d orbitals (Sec. II B), and the γ state is assigned to dz2. For such a multiorbital impurity, the energy of a given YSR peak depends on the full spin Hamiltonian—spin magnitude S, uniaxial and transverse anisotropy, spin–orbit coupling—and on orbital-dependent hybridization, not only on a scalar J. Therefore, site-to-site variations in the Fe spin state, in magnetic anisotropy, or in orbital occupation could generate the observed 0.10–0.49 meV spread in εγ even if the scalar exchange coupling of Eq. (1) were constant. Such variations would still be 'crystal-field' effects in a broad sense, but they would not establish the specific claim that the YSR shifts are a readout of exchange-coupling variations caused by Nb displacements. The paper neither measures the spin state/anisotropy at each binding site nor fits the full multiplet with a multiorbital model. A second unresolved premise is that the bare-surface dI/dV at Vbias = 5 mV (after Bragg-peak removal) is a quantitative proxy for the Fermi-level LDOS at the Fe adsorption site; hybridization matrix elements can vary while the bare LDOS does not. The central structural conclusion is thus not uniquely determined by the data.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports an STM atom-manipulation study in which an individual Fe adatom is placed on 225 nominally equivalent hollow sites of 2H-NbS2 and probed with Yu-Shiba-Rusinov (YSR) spectroscopy using a superconducting V tip. The authors find that the energy of the strongest YSR state (γ) varies between 0.10 meV and 0.49 meV across the map, while the superconducting gap, Josephson conductance, and local-density-of-states maps appear uniform or uncorrelated with the variation. After ruling out spatial variations of Δ, the bare-surface LDOS, and potential-scattering asymmetry, they conclude that the residual variation is dominated by spatial changes of the exchange coupling J, which they interpret as crystal-field modulations caused by defect-induced displacements of Nb atoms. They propose the method as a new atomic-scale probe of hidden lattice distortions in an incipient charge-density-wave material.","tokens_in":19109,"tokens_out":5285,"duration_ms":49376,"significance":"If the central attribution is correct, the paper introduces a genuinely new and highly sensitive probe of atomic-scale crystal-field modulations, with potential applicability to incipient-CDW and incipient-ferroelectric materials. The experimental work is substantial: 225 binding sites are measured; the tip-position control yields a standard deviation of 3 μeV; z-dependent spectroscopy shows that peak positions do not shift with tip height; the superconducting gap and Josephson conductance are checked for uniformity; and the deconvolution procedure is validated against the raw spectra. These controls make the raw observation—a large, position-dependent spread of εγ—very credible. However, the inference from that observation to exchange-coupling variations and Nb displacements rests on a model assumption that is not justified for the multiorbital Fe sensor. The significance is therefore conditional: the sensing method and the observation are likely to be valuable, but the specific physical interpretation needs either additional theoretical support or an explicit softening.","major_comments":[{"comment":"The exclusion argument is built on Eq. (1), the classical single-spin YSR formula. However, the Fe sensor is introduced in §II B as a multiorbital impurity with four YSR pairs (α–δ) arising from crystal-field-split d orbitals, with the γ state assigned to dz2. For such an impurity, the energy of the γ resonance is set by the full impurity spin Hamiltonian (S, magnetic anisotropy, spin–orbit coupling) and by orbital-dependent hybridizations, not by the single product Sρ0J that appears in Eq. (1). Consequently, site-to-site changes in the Fe spin state, magnetic anisotropy, or orbital occupation—all crystal-field effects in a broad sense—could produce the observed 0.10–0.49 meV spread in εγ even if the scalar exchange coupling J were constant. The paper neither measures S or the anisotropy at each binding site nor fits a multiorbital model. The conclusion that the residual variation is dominated by exchange-coupling changes and, further, by Nb displacements is therefore not established by the presented exclusion analysis. I recommend either adding a model or calculation that justifies the single-spin reduction for the γ state, or softening the claim to 'variations in the local crystal-field environment' and explicitly labeling the Nb-displacement interpretation as speculative.","section":"§II C, Eq. (1)"},{"comment":"The LDOS-uncorrelation test uses dI/dV maps of the bare surface at Fe-free hollow sites. The quantity that enters Eq. (1) is ρ0 at the impurity site in the presence of the adatom, including orbital-specific hybridization between the Fe d states and the substrate. A constant-current topographic/Friedel map at V_bias = 5 mV is not demonstrated to be a faithful proxy for this quantity. While the absence of correlation at eight energies is suggestive, the paper never validates the proxy directly, for example by measuring the LDOS at the Fe position before and after deposition or by checking orbital-resolved YSR maps. This weakens the otherwise careful exclusion of the ρ0 term.","section":"§II C, Fig. 3d and Fig. S8"},{"comment":"The potential-scattering exclusion is also model-dependent. In the classical formula, the asymmetry of the two YSR peaks is governed by B = πρ0K; for a multiorbital impurity with several YSR pairs, the intensity asymmetry of one orbital-derived state need not map cleanly onto a scalar K, and the observed linewidth has an additional lifetime contribution (Ref. [59]) that is energy dependent. The near-symmetric A_YSR and the small variation of Γ_YSR are reasonable qualitative evidence, but they do not close the exclusion in the same quantitative way that the text implies.","section":"§II C, Fig. 4c,d"}],"minor_comments":[{"comment":"The caption says the dI/dV maps were recorded at V_bias = −200 mV and −200 mV; the second value should presumably be +200 mV.","section":"Fig. S2 caption"},{"comment":"The symbol B is used for the potential-scattering parameter in Eq. (1), while A_YSR denotes the measured YSR intensity asymmetry in Fig. 4c; this notation is confusing and should be changed to avoid implying that A_YSR is the same A as in Eq. (1).","section":"Eq. (1) and Fig. 4c"},{"comment":"The deconvolution parameters (Δ_tip, Γ) are given for one representative spectrum; please state explicitly whether the same values were used for all 225 spectra and how any drift or tip changes over the long measurement sequence were handled.","section":"Fig. S4 and §S3 B"},{"comment":"Some binding sites show only three scatter points because a state is degenerate or too weak to fit; please state how unresolved states were treated in the Gaussian fitting and whether the sorting of binding sites by εγ is affected by this.","section":"Fig. 4a"},{"comment":"The sentence 'we still found a varying sample quality, depending on the cleave and positioning of the tip on the crystal' should be rephrased, since sample quality cannot depend on tip positioning; the intended meaning is presumably the choice of measurement area on the cleaved surface.","section":"§S2, first paragraph"}],"recommendation":"major_revision","confidential_remarks":"The experimental dataset is strong and the control measurements are unusually thorough; the raw observation of a large, structured spatial variation of εγ is credible. The main gap is conceptual: the classical single-spin formula of Eq. (1) is used to interpret a multiorbital Fe sensor that the paper itself describes as having four crystal-field-split YSR pairs. If the authors are willing to substantially soften the central attribution—or, better, support it with a multiorbital calculation—the paper could become publishable. The current version overclaims the link between the measured YSR shifts and Nb displacements, and that overclaim is load-bearing for the abstract and conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this paper has a genuinely new measurement with unusually careful controls, and the headline interpretation is more expansive than the data strictly require, but the authors are candid about the speculative part. It deserves a serious referee and probably publication with some rewording.\n\nThe new thing is a 225-site map of YSR excitation energies made by dragging a single Fe atom across equivalent hollow sites on 2H-NbS2. The gamma state shifts between 0.10 and 0.49 meV across an 8x4 nm area, spanning about 70% of the inner gap, and this variation does not track the measured LDOS modulations or the YSR intensity asymmetry. The controls are the strongest part: 21 tip positions on one atom give a 3 micro-eV spread, z-dependent spectra leave peak positions unchanged, and the LDOS analysis is Fourier-filtered and checked at ten energies. The Josephson data and uniform gap argue against order-parameter or pairing-density variation. That is solid, careful work.\n\nThe soft spot is the attribution step. Equation (1) is the classical single-spin YSR formula, but the Fe sensor shows four YSR pairs from crystal-field-split d-orbitals. Site-to-site changes in the spin state, magnetic anisotropy, or orbital occupation could shift epsilon_gamma without requiring a change in the scalar exchange coupling J. So the specific conclusion that \"exchange coupling J is spatially varying\" and the further leap to Nb displacements are not uniquely determined. That said, the paper itself flags the Nb origin as speculative, and a site-to-site spin-state change would still be a crystal-field effect in the broad sense. The abstract's \"we determine the main contribution originates from variations in the local crystal-field environment\" is a bit stronger than the exclusion argument warrants. I'd like to see either a multiorbital model or softer wording, and the promised Zenodo data should appear before final acceptance.\n\nMinor: the bare-surface dI/dV at 5 mV is used as a proxy for the Fermi-level LDOS at the adatom; it is checked at several energies but never validated directly against the YSR coupling site. This is a minor gap because the correlation plots are flat, but worth a sentence.\n\nOverall: the measurement is the contribution, and it is a good one. The paper will be read by the STM/YSR community and by people working on incipient CDW materials. Send it to review; the fixes are wording and data availability, not new experiments.","headline":"A careful, genuinely new YSR sensor map on 2H-NbS2 whose interpretation is broader than its exclusion argument strictly supports, but the authors know it and the measurement is worth refereeing.","tokens_in":19836,"tokens_out":2675,"would_cite":true,"duration_ms":23032,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper uses individual Fe adatoms as movable atomic-scale sensors to show that Yu-Shiba-Rusinov excitation energies vary strongly across 225 crystallographically equivalent hollow sites on 2H-NbS2, and argues that the dominant cause is…","keywords":["Yu-Shiba-Rusinov states","2H-NbS2","crystal-field modulation","scanning tunneling microscopy","atom manipulation","incipient charge-density-wave","exchange coupling","lattice distortion"],"falsifier":"The central claim would be falsified if an Fe atom shuttled across 225 equivalent sites in a region verified to be free of surface and subsurface defects still showed the same roughly 0.39 meV spread in gamma-state energy, since the proposed cause, defect-induced lattice relaxation, would be absent.","tokens_in":18536,"feed_emoji":"🧲","tokens_out":6152,"duration_ms":52290,"temperature":0.7,"pith_summary":"This paper tries to establish that a single magnetic iron atom can act as an atomic-scale probe of hidden crystal-field variations in the superconductor 2H-NbS2, a material sitting on the verge of a charge-density-wave transition. By dragging one Fe atom across 225 equivalent hollow sites with an STM tip, the authors find that the energy of its strongest Yu-Shiba-Rusinov excitation moves between 0.10 meV and 0.49 meV even though the superconducting gap, the Josephson conductance, and the local density of states remain nearly uniform. They argue by elimination, ruling out gap variations, LDOS modulations, and potential scattering, that the shifts come from site-dependent exchange coupling, which reports local changes in the crystal field. The conclusion matters because it implies that intrinsic point defects reshape the lattice over nanometer scales in a material close to a CDW instability, and that mobile magnetic atoms are a general sensor for such distortions.","feed_headline":"An iron atom maps hidden lattice distortions in 2H-NbS2","feed_subtitle":"YSR energy shifts from 0.10 to 0.49 meV over identical sites, tracing crystal-field changes invisible to STM.","key_machinery":"The central object is the Yu-Shiba-Rusinov (YSR) bound state, the sub-gap excitation formed when a magnetic impurity exchange-couples to a superconductor. Its energy is described by the classical-spin formula $\\epsilon_{YSR} = \\Delta(1-A^2+B^2)/\\sqrt{(1-A^2+B^2)^2+4A^2}$, where $A = \\tfrac{1}{2}\\pi S\\rho_0 J$ is the exchange coupling and $B = \\pi\\rho_0 K$ is the potential scattering. This formula ties the excitation energy to the superconducting gap $\\Delta$, the normal-state density of states $\\rho_0$, the potential-scattering coefficient $K$, and the exchange coupling $J$. The measurement protocol, moving one Fe atom to 225 equivalent hollow sites, deconvolving the superconducting-tip spectra, and Gaussian-fitting the gamma resonance, turns the formula into a site-resolved sensor: after independently bounding $\\Delta$, $\\rho_0$, and $K$, the residual energy shifts are attributed to $J$, meaning the crystal-field environment.","core_discovery":"The central claim is that the spatial variation of Yu-Shiba-Rusinov excitation energy for Fe atoms on 2H-NbS2 is dominated by variations in the local crystal-field environment, not by any electronic inhomogeneity of the superconducting state. The evidence is a manipulation experiment: one Fe atom placed on 225 equivalent hollow sites shows gamma-state energies spanning about 70 percent of the inner superconducting gap, with the defect site giving the lowest energies but significant shifts appearing nanometers away. The experimental controls exclude the standard alternatives: the two-gap BCS spectrum is spatially homogeneous, the Josephson conductance is uniform, the Fermi-level dI/dV signal varies by only about five percent with no correlation to the YSR energy, and the YSR intensity asymmetry shows no potential-scattering trend. What remains is a spatially varying exchange coupling, and since that coupling is set by the overlap of the adatom d-orbitals with the surrounding crystal field, the paper concludes that the lattice is locally distorted around defects, most plausibly through small displacements of Nb atoms, consistent with the soft phonon physics that places 2H-NbS2 near a CDW instability.","pith_inferences":["A quantitative step would be to convert measured YSR energy shifts into displacements: first-principles calculations of the exchange coupling $J$ as a function of Nb atomic positions could calibrate the sensor in picometers, something the paper does not do.","The same manipulation protocol could be applied near step edges, grain boundaries, or artificial defect arrays to separate long-range elastic relaxation from electronic scattering, testing whether the inferred distortions are purely defect-induced.","If the observed site-to-site spread scales with the density of surface and subsurface sulfur vacancies across different crystals, that would confirm the long-range lattice-relaxation scenario; if it persists in extremely clean regions, the origin would need revision."],"forward_implications":["YSR spectroscopy with manipulated magnetic adatoms becomes a general atomic-resolution probe of crystal-field and strain variations, not just of magnetic coupling.","Regions that appear flat and defect-free in topography can still host substantial lattice relaxation, so standard STM imaging underestimates structural heterogeneity in incipient CDW materials.","The defect response of 2H-NbS2 encodes its proximity to a CDW instability: local lattice relaxations around sulfur vacancies behave like nanoscale precursors of the charge-density-wave distortion.","Because the $d_{z^2}$-derived gamma state is the most sensitive channel, the method offers orbital selectivity: different YSR multiplets can report on different crystal-field components."],"supporting_citations":[{"why":"Supplies the classical-spin YSR energy formula that the analysis uses to separate exchange coupling from gap, density of states, and potential scattering.","marker":"[36-38]"},{"why":"Provides the multi-gap superconducting parameters of 2H-NbS2 used to quantify the gap size and the roughly 70-percent-of-inner-gap scale of the YSR shift.","marker":"[30]"},{"why":"Establishes the binding sites and YSR fingerprints of Fe on the isostructural CDW material 2H-NbSe2, the comparison basis for the observed variation magnitude.","marker":"[45]"},{"why":"Gives the anharmonic-phonon picture of 2H-NbS2 as an incipient CDW system, the context for interpreting lattice relaxations.","marker":"[29]"},{"why":"Predicts CDW-relevant Nb displacements and soft phonons in 2H-NbS2, supporting the proposed Nb-sublattice distortion.","marker":"[34]"},{"why":"Reports impurity-pinned incommensurate CDW behavior in 2H-NbS2, motivating the search for defect-induced lattice response.","marker":"[35]"},{"why":"Defines the Dynes-broadened BCS lineshape used to fit the superconducting gap and to deconvolve the superconducting-tip density of states from YSR spectra.","marker":"[51]"},{"why":"Provides the orbital assignment of YSR multiplets on transition-metal adatoms, used to identify the gamma state with the $d_{z^2}$ orbital.","marker":"[57]"}],"fun_headline_variants":["Single iron atom on 2H-NbS2 reveals crystal-field distortions","Iron atom acts as sensor to map hidden lattice distortions in superconductor","YSR energy shifts expose crystal-field modulations near defects in 2H-NbS2","One adatom, 225 sites: crystal-field shifts unveiled in 2H-NbS2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the classical single-spin YSR formula with one exchange parameter $J$ adequately describes a multiorbital Fe atom that actually shows four YSR pairs; if the spin state, magnetic anisotropy, or multiorbital structure changes from site to site in ways not captured by the LDOS and asymmetry checks, the residual variation need not be due to crystal-field-modulated exchange coupling.","fun_headline_variants_meta":{"raw":{"variants":["Single iron atom on 2H-NbS2 reveals crystal-field distortions","Iron atom acts as sensor to map hidden lattice distortions in superconductor","YSR energy shifts expose crystal-field modulations near defects in 2H-NbS2","One adatom, 225 sites: crystal-field shifts unveiled in 2H-NbS2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000788,"raw_usage":{"total_tokens":3508,"prompt_tokens":1014,"completion_tokens":2494,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":2403}},"tokens_in":630,"tokens_out":2494,"duration_ms":16261,"temperature":1.0,"reasoning_tokens":2403,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:23:41.826199+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The central claim would be falsified if an Fe atom shuttled across 225 equivalent sites in a region verified to be free of surface and subsurface defects still showed the same roughly 0.39 meV spread in gamma-state energy, since the proposed cause, defect-induced lattice relaxation, would be absent.","supporting_citations":[{"cited_title":"Guillam´ on, H","cited_arxiv_id":null,"evidence_quote":"Provides the multi-gap superconducting parameters of 2H-NbS2 used to quantify the gap size and the roughly 70-percent-of-inner-gap scale of the YSR shift."},{"cited_title":"Liebhaber, S","cited_arxiv_id":null,"evidence_quote":"Establishes the binding sites and YSR fingerprints of Fe on the isostructural CDW material 2H-NbSe2, the comparison basis for the observed variation magnitude."},{"cited_title":"Leroux, M","cited_arxiv_id":null,"evidence_quote":"Gives the anharmonic-phonon picture of 2H-NbS2 as an incipient CDW system, the context for interpreting lattice relaxations."},{"cited_title":"Bianco, I","cited_arxiv_id":null,"evidence_quote":"Predicts CDW-relevant Nb displacements and soft phonons in 2H-NbS2, supporting the proposed Nb-sublattice distortion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports impurity-pinned incommensurate CDW behavior in 2H-NbS2, motivating the search for defect-induced lattice response."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the orbital assignment of YSR multiplets on transition-metal adatoms, used to identify the gamma state with the $d_{z^2}$ orbital."}],"review_version":1}